Unit 2 Test (practice)
AP Statistics
Name:
1. The heights of American men aged 18 to 24 are approximately Normally distributed with mean 68 inches and
standard deviation 2.5 inches. Half of all young men are shorter than
(a) 65.5 inches
(b) 68 inches
(c) 70.5 inches
(d) can’t tell, because the median height is not given
(e) none of the above
2. Use the information in the previous problem. Only about 5% of young men have heights outside the range
(a) 65.5 inches to 70.5 inches
(b) 63 inches to 73 inches
(c) 60.5 inches to 75.5 inches
(d) 58 inches to 78 inches
(e) none of the above
3. For the density curve shown to the right,
which statement is true?
(a) The area under the curve is 1.
(b) The density curve is symmetric.
(c) The density curve is skewed right.
(d) The density curve is Normal.
(e) None of the above is correct.
4. For the density curve shown in Question 3, which statement is true?
(a) The mean and median are equal.
(b) The mean is greater than the median.
(c) The mean is less than the median.
(d) The mean could be either greater than or less than the median.
(e) None of the above is correct.
5. The area under the standard Normal curve corresponding to –0.3 < z < 1.6 is
(a) 0.3273
(b) 0.4713
(c) 0.5631
(d) 0.9542
(e) none of the above
6. A Normal density curve has which of the following properties?
(a) It is symmetric.
(b) It has a peak centered above its mean.
(c) The spread of the curve is proportional to it standard deviation.
(d) All of the properties (a) to (c) are correct.
(e) None of the properties (a) to (c) is correct.
7. Suppose you and 999 other people take a test. Your score of 63 (out of 100) is the 73rd percentile. This means
(a) at least 73% of the people scored 63 or better.
(b) at least 270 people scored 73 or better.
(c) at least 730 people scored 73 or better.
(d) at least 27% of the people scored 73 or worse.
(e) at least 270 people scored 63 or better.
8. Which of the following histograms would be best approximated by a Normal distribution?
(a)
(b)
(c)
(d)
(e) All of (a) through (d)
9. For the density curve shown, which statement is true?
(a) The density curve is roughly symmetric.
(b) The density curve is skewed right.
(c) The density curve is skewed left.
(d) The density curve is Normal.
(e) None of the above is correct.
10. For the density curve shown in Question 9, which statement is true?
(a) The mean is greater than the median.
(b) The mean is less than the median.
(c) The mean and median are equal.
(d) The mean is probably equal to the median.
(e) None of the above is correct.
11. Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal
distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will
contain between 16.0 and 16.1 ounces is about
(a) 10
(b) 16
(c) 34
(d) 68
(e) none of the above
12. This is a continuation of Question #11. Approximately what percent of the bags will be less than 15.9 oz?
(a) 84
(b) 16
(c) 32
(d) 50
(e) none of the above
13. The plot shown at the right is a Normal probability plot for a set of data. The data value is plotted on the x
axis, and the standardized value is plotted on the y axis. Which statement is true for these data?
(a) The data are clearly Normally distributed.
(b) The data are approximately Normally distributed.
(c) The data are skewed to the left.
(d) The data are skewed to the right.
(e) There is insufficient information to determine the shape of the distribution.
14. The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test that measures the
degree to which Mexican Americans are adapted to Mexican/Spanish versus Anglo/English culture. The range
of possible scores is 1.0 to 5.0, with higher scores showing more Anglo/English acculturation. The distribution
of ARSMA scores in a population used to develop the test is approximately Normal with mean 3.0 and
standard deviation 0.8.
(a) Sketch the density curve of this Normal distribution, with the scale clearly marked on the horizontal axis.
(b) What proportion of the population used to develop the test has scores between 1.7 and 2.1? Show all work.
(c) How high a score on this test must a Mexican American obtain to be among the 30% of the population used
to develop the test who are most Anglo/English in cultural orientation? Show your method.
15.
Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally
distributed with mean 110 and standard deviation 25. Scores for the 60 to 64 age group are approximately
Normally distributed with mean 90 and standard deviation 25.
a) Sarah, who is 30, scores 135 on this test. Sarah's mother, who is 60, also takes the test and scores 120. Who
scored higher relative to her age group, Sarah or her mother? Use appropriate calculations to justify your
answer.
b) What would a 61-year-old have to score on the Wechsler Adult Intelligence Scale in order to be in the top
5% of her age group?
c) What would a 22-year-old have to score to be at the 25th percentile?
d) Briefly explain what is meant by the word “percentile” in #15c.